MAXIMUM DISTANCE OF A LINE FROM A POINT

UR QUESTIONS, OUR SOLUTION: 2

Find the equation of a line passing through (1,2) and having maximum distance from the point (3,1). (COR/M)

( asked by ESHA PRASHAR)

SOL: 

We can solve this problem in two different ways one is using Graphs and other by Conventional method.

GRAPHICAL METHOD

we already know we will have infinetly many lines passing through (1,2), so let's examine all those lines and picked the one having maximum distance from point (3,1).Clearly the line perpendicular to line joining (1,2) and (3,1) is the required line having maximum distance from (3,1).( shown by bold line).

Therefore,the slope of the required line is -(3-1)/(1-2)=2. Hence the line will be (y-2)=2 (x-1) or y=2x.

CONVENTIONAL METHOD

The general equation of line passing through (1,2) is y=mx+2-m. Its distance from (3,1) will be

d=|2m+1|/sqrt(msq+1) where sqrt is square root and m sq is m square.

differentiating d with respect to m, we will get m=2 as the point of maxima.

Therefore, the required will be y=2x.